In December, representatives of the U.S., China and Afghanistan met for private talks in London, the first time the three countries convened to seek ways to forge peace in Afghanistan, a senior U.S. official said.

The previously undisclosed meeting, which came within days of a visit by the Afghan Taliban to Beijing, was a step on a path long resisted by China, wary of the U.S. military presence in Afghanistan and reluctant to meddle in its neighbor’s affairs. The three countries met again last month at an international meeting...